The Belgian side restricted the Red Devils to a 1-1 draw in last week's quarter-final first leg in Brussels, meaning that the tie remains delicately poised heading into this evening's reverse fixture.
Weiler is under no illusion of the task facing his charges, however, and says that Anderlecht must produce the "perfect" display if they are to have any hope of pulling off a big shock at the Theatre of Dreams.
"Of course we have to believe," he told reporters. "We do believe, but at the same time we have to be realistic. We know we are playing a very high level team in Manchester United. You only have to look at the performance of this squad last Sunday - they limited Chelsea to hardly any shots on target at all.
"I think they have had three defeats in the entire season and in the last 22 matches in the game they are unbeaten. They are very strong at the back and they have some great individuals as well.
"We saw in the first leg what they can do and we know it is going to be very hard, and we know that pretty much everyone in our team is going to have to put in a perfect performance. But we do believe and we will be trying our absolute best to try and make sure that happens. We do need a goal but we need to be prudent as well."
Weiler also hinted that he will field a weakened side against United on Thursday night, with focus instead on the Belgian top flight.